Cristian Chivu had given the Nerazzurri the lead from a free-kick but two goals from ex-Inter man Meggiorini soon turned the game on its head, only for Esteban Cambiasso to find the equaliser to spare the home team's blushes.
Torino did go close to winning the game, but head coach Giampiero Ventura will nonetheless be satisfied with a point which cements his side's position in mid-table.
Inter took the lead early on through Chivu, after Torino's protests were dismissed when Antonio Cassano went to ground easily on the edge of the penalty area.
From the resultant free-kick, the Romanian defender curled the ball over the wall and beyond the reach of Jean-Francois Gillet.
Rather than looking to build on their lead, though, Inter sat back and invited pressure on to themselves.
Torino duly obliged and struck back in the 24th minute through Meggiorini, who rifled in from the edge of the penalty area after Fredy Guarin lost possession cheaply.
Meggiorini came through the Nerazzurri's youth ranks and has made a habit of punishing his former club.
He did so again in the 52nd minute when he put the Granata in front.
Alessio Cerci delivered an inch-perfect cross from the right which Meggiorini met at the near post and, with the inside of his right foot, he guided it into the far corner.
It was now Inter's turn to chase the game and Cambiasso missed a good chance to level in the 62nd minute when he lifted a shot over the crossbar from eight yards out.
He did not waste his next chance, though, bringing Inter level in the 66th minute with a simple tap-in after Javier Zanetti had done all of the hard work to get to the goal-line before pulling the ball across to his team mate.
Torino were not going to settle for a point and a fine one-handed save from Samir Handanovic prevented substitute Rolando Bianchi from putting them in front again in the 71st minute as he pushed the ball onto a post.
Il Toro nearly snatched all three points, but Meggiorini was denied his hat-trick by Handanovic.